Disagree. Bounded rationality is neither maximizing or satisficing - it’s sort of a middle ground. Yes, the point is to maximize utility in a “big picture” sense, as @adamwolf points out, by including consideration of resources, but that’s not what maximizing is. It’s also not what satisficing is.
Specifically, we’re talking about procedures for choosing one option of a set of multiple options.
I’ll illustrate with @mkalbert’s restaurant example:
Maximizer: there are 40 things on the menu. I’m going to read over each one and choose the best.
Satisficer: I’m going to look through the menu. Once I find one thing that’s good enough, I’ll order it.
Bounded rationality: in this context it doesn’t make sense to spend more than a few minutes choosing an option. So I’ll use those few minutes to first come up with a way of deciding and then decide. I know this restaurant is known for X, I’m kinda craving Y, and I’ve heard good things about Z, so I’ll restrict my choices to the 10 things that are close to X, Y, or Z. I don’t have time to choose the absolute best, so I’ll narrow further to a few that seem like they’d be good enough, and then I’ll pick the best of those few.
Or, put another way:
Maximizing means your goal is to choose the best option at all costs.
BR means your goal is to choose the best option given limited resources, and you will therefore use heuristics as shortcuts at the cost of possibly missing the best option.
Satisficing means you don’t care about choosing the best option. That’s not even a consideration. You just want to choose an option that’s good enough. It’s a completely different way of thinking.
I see satisficing as lazy and myopic. It’s being complacent. A satisficer isn’t willing to spend another minute looking at multiple “good enough” options. That might save time now, but could cost you later on if you end up needing to switch, or if another minute of looking would have revealed an option that would have been significantly better.
Sure, you could think of satisficing as a specific extreme BR strategy to be used in unusual situations with very limited resources (I hold a gun to your head - choose one NOW).
Also see: Secretary problem - Wikipedia